I have a doubt about the following definition of pronilpotent differential graded Lie algebra found e.g. in Willwacher (Def. 2.21) and Lazarev-Markl (Def. 7.1):
Definition: A pronilpotent (or: complete in Lazarev-Markl) differential graded Lie algebra is an inverse limit of finite dimensional nilpotent differential graded Lie algebras.
Does anyone know if we are allowed any limit, or can we take only sequential limits indexed by $\mathbb{Z}$, i.e. $$\mathfrak{g}:=\varprojlim_n \mathfrak{g}_n\longrightarrow\ldots\longrightarrow\mathfrak{g}_{n+1}\longrightarrow\mathfrak{g}_n\longrightarrow\ldots,$$ or still something else?